Mathiness: A Guide for the Perplexed

From my twitter feed at the annual American Economic Association meetings, we knew it was coming: Paul Romer (the founder of endogenous growth theory) had levelled an attack on many macroeconomic theorists including his advisor Bob Lucas. The nature of this attack would have to arrive in May when the article appeared in the American Economic Review (Paper and Proceedings). And here it is. 5 pages of strong language that we haven’t seen in economics in decades. To be sure, this is SFW but it is the “calling out” Romer is doing that is unusual.

There is part of me that really enjoys seeing this. Somehow I think we have lost the ability to use our journals and conferences to express frustrations with the direction of the profession. This is the same way I felt about Piketty’s book. It is something that was more common in a bygone age and is missing today.

But, I have to guess, many younger members of the profession will likely be somewhat perplexed about precisely what Romer is upset about. It took me a few reads to posit some theory of that myself. So I thought here I would try and explain my take on his critique in a way that might explain to others what is going on.

Romer is going all meta on us. He things that economic theory, mainly macroeconomic theory, is itself in a bad equilibrium.

In choosing to present the theory in less detail, they too may have responded to the expectations in the new equilibrium: empirical work is science; theory is entertainment. Presenting a model is like doing a card trick. Everybody knows that there will be some sleight of hand. There is no intent to deceive because no one takes it seriously. Perhaps our norms will soon be like those in professional magic; it will be impolite, perhaps even an ethical breach, to reveal how someone’s trick works.

Romer here is not saying that theory should be entertainment but instead that it has become entertainment. This is the notion of mathiness. What researchers he cites are doing, Romer argues, is dressing up an idea they want to convey in mathematics and presenting that as a logical theoretical insight. The article is scant on details but an online appendix does this more thoroughly: some key parts of the models written down by some very famous people in the field are presented loosely or, at worst, incorrectly. In other words, theory has become a relatively sloppy thing and, at best, a sideshow to some other game.

I think there is something to that view. I remember my advisor, Paul Milgrom, holding my feet to the fire when I used general equilibrium models with monopolistic competition and solved them by appealing to the “infinitely small” nature of agents or goods. I retorted that all of the other economists I was relying upon did this from Krugman to Shleifer and the like. But that wasn’t good enough. So I spent some time trying to hunt down why others had “got away with this assumption” while I was being made to suffer. As it turned out, there, in the footnote of Romer’s paper, was the answer. He had worried about this but so had someone else and he provided a citation. As these things were meant to happen, I stood on the shoulders of others to avoid having to reinvent what was going to be a very painful wheel.

There was another time in my career that I was not so lucky. I had relied on a theorem in a published paper for my own proof but, as it turned out, that proof was incorrect. Specifically, an equilibrium I thought was unique wasn’t. This was no great issue but it was an issue for others who were evaluating my paper and realized the mistake in the published paper. It was my job, they claimed, to fix it as they found the notion of a unique equilibrium would make my paper more attractive. There was no fix and the paper was rejected. To this day, there has been no retraction or even qualification to the published paper.

Thus, Romer’s first thesis is that mathiness is becoming more pervasive in economics. This is something worth testing. Romer’s observations and my own anecdotal thoughts do not necessarily mean that there is a pervasive problem here and, indeed, that is exists beyond growth theory or some other limited domains. But mathiness (aka sloppy thinking dressed up in maths) does undermine science and diminishes the role of theory. Theory is a powerful tool for yielding precise insights about the world and also important normative conclusions for policy — especially when insufficient data exists.

But there is a second thesis to Romer and that is that mathiness is a device being used by academics to further a political agenda rather than purely the pursuit of science. Here his thinking is murkier and so I had to actually look at the papers he was critiquing to guess at what the association might be. The papers themselves reveal a little but not much. Here, for instance, is the key section from Lucas and Moll that deals with Romer’s issues:

It is worth noting that with the decentralized vision of knowledge we have adopted, there is always an incentive to seek more knowledge. In much existing endogenous growth theory, in contrast, knowledge is “nonrival” in the sense that it can be costlessly replicated and used by any number of people simultaneously. As first noted by Romer (1990), an immediate implication of nonrivalry is that under perfect competition, no one would invest in knowledge creation. In our setup, in contrast, knowledge is partially rival: it is “rival” in the short run because people who want to access better knowledge must exert effort and have the good luck to run into the right people; but knowledge is “nonrival” in the long run in the sense that it is in no way diminished when it spreads from one person to another. Agents exert positive search effort even under perfect competition because the search friction precludes the immediate diffusion of existing knowledge. This seems to us a step toward descriptive realism. Of course, to say that the private return to search is positive is not to say that it equals the social return.

And here is a key footnote:

Using a somewhat different terminology, we may say that knowledge is “embodied” in individual people in the short run but “disembodied” in the long run because it outlives any one individual. Romer (1990) noted that knowledge that is tied to a specific person human capital is necessarily rival because that person cannot be in more than one place at the same time. Elsewhere, Romer also listed as an attribute of a purely nonrival good that it can be costlessly replicated. In our setup, in contrast, replication requires costly search effort.

So what Lucas and Moll have done have provided a model where it is theoretically possible for knowledge to be created under perfect competition. This is in contrast to Romer’s model where this could not occur but could occur if there was imperfect competition. Romer’s point is that there actually is such imperfect competition and so we don’t need yet another model as to why knowledge can be created under perfect competition. There may be some interesting mechanism to the Lucas and Moll approach but the fact that it works under perfect competition is surely beside the point.

The problem is this: when you can demonstrate that something occurs under perfect competition, there is a belief that you are somewhat absolved from saying that there is a policy problem although as there are externalities present, Lucas and Moll favour taxation to boost growth. And who should the taxation system promote? Teachers. It isn’t at all clear what they are driving at for the real world. Maybe some glorified monster.com or do they want to subsidize Linked In. In any case, I am not sure that effort was worthy of space in the Journal of Political Economy. You see, I can get crochety too.

The drive to perfect competition tends to reduce the scale of the problem and diminish its significance. Endogenous growth theory demonstrated how the persistence of growth and the notion that the private rate of return to basic knowledge creation is less than its social return is a pervasive part of the system even when we use instruments like intellectual property protection to try and correct the distortion. How to accelerate knowledge creation is a hard problem that won’t be solved by taxing an externality here or there. There is more, much more, to it than that and mathiness and its tendency to direct people towards the wrong questions (can this work even under perfect competition?) and away from the right (what is the mechanism driving knowledge creation and diffusion?) is the proverbial drunk search for keys under a lamp post.

Nonetheless, outside of macroeconomics, I am not sure that it is politics as much as some narrow thinking driving theorists to produce big papers with big empirical implications (competing for limited space in top journals) rather than slowly and surely getting the details right (and publishing incremental changes) that may have given rise to mathiness. In other words, my guess is that the organization of our knowledge in economics leaves alot to be desired and is distorting the way that knowledge is being created. I would love to see Romer’s paper and others put us on a path to discussion of all of that.

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9 Replies to “Mathiness: A Guide for the Perplexed”

One serious flaw in most economics models, it seems to me, is that things they assign as fundamentals are not, in fact, fundamental, but are abstractions related to but not equivalent to fundamentals. Other fundamentals are, astonishingly, not included in models at all.

In physics and chemistry, one can do calculations that are far from their quark and proton fundamentals — for instance, mixing proportions of vinegar and baking soda to produce a perfectly acceptable geyser for the kids. But if pressed, chemists and physicists can lead you all the way down to quantum, where you will both be perplexed, but at least perplexed in the same way every time.

Try that with economics. Analyses that pretend to be fundamental often stop at GDP, profits, hours of work, unemployment rates, the Fed rate, and so on. But the quarks of economics are the energies, time, attention and abilities of individual human beings. The fundamental “interest rates” at that level are childbearing and education, health, excess energy and possessions beyond sustenance, information and tradition, and things of that sort.

Whether salt or freshwater, no Econ model can be complete and trustworthy if it doesn’t now and then tunnel down to the quark level. I’m waiting with bated breath to witness this.